BUILDING FRACTIONS: Example 2

Rule 17:
To build a fraction is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction so that you can reduce, you insert a 1 and build.

Example 3:
Create a fraction with 40 in the denominator that is equivalent to the fraction tex2html_wrap_inline46 .
Answer:
The answer is the fraction tex2html_wrap_inline48 .

Solution:
This problem is a little more difficult because you can't multiply 50 by an integer to get 50. So we will first reduce the initial fraction. Reduce tex2html_wrap_inline46 . tex2html_wrap_inline52 .
tex2html_wrap_inline46 is equivalent to tex2html_wrap_inline56 . (You can verify this with your calculator.)
Recall that you can multiply any number by 1 without changing the value of the number. (Rule 6).
Multiply the fraction tex2html_wrap_inline56 by 1.
Recall that 1 has many forms, look for the form of 1 that will result in a denominator of 40.

Since 5 tex2html_wrap_inline60 8 = 40, use the fraction tex2html_wrap_inline62 as 1.
Now tex2html_wrap_inline64 can be written as tex2html_wrap_inline66 . The product is tex2html_wrap_inline48.

We have created a fraction with a denominator equal to 40 that is equivalent to the fraction tex2html_wrap_inline46 .

Check:
Now prove to yourself with your calculator that your answer is correct. Calculate 80 divided by 50 and calculate 64 divided by 40; both should yield the same answer. If you are correct, the answers are the same (equivalent) and you have successfully built a fraction.

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Author:Nancy Marcus

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